Introduction

Originating in Belgium or France in the late 1600’s, the french-fry has been around longer than the United States. While the origination is disputed, our research team is interested in the modern-day french-fry. The french-fry’s long history has created the opportunity for a large number of variants: The waffle fry, the steak fry, the curly fry, etc. To limit the scope of our research we set our sights on the traditional, standard cut fry. The standard cut fry is evenly cut, medium-thin, and only fried once.

We want to know how different American fast-food chain’s fries compare. Using properties like weight, width, length, height, and cost, we can find the mean fry of each brand. Then we can compare different companies mean fry to find the best value fry. While subjective, the best value fry has the lowest cost per fry density. In more simple terms, we are asking “Which American fast-food company gives the most fry per dollar?”

Methodology and Data Collection

We decided to compare 4 major American fast-food companies: McDonalds, Carl’s Jr., Burger King, and Wendy’s. Our process involved ordering a large fry then measuring the weight, length, width, and height of each fry. The population we are studying is the “average fry” from each of these restaurants in the Millcreek, UT area (NOT the “average french fry order”).Due to budgetary constraints, a single order of large fries was procured from each location. While it would have been nice to discuss “which restaurant has the best order of fries?”, this would have required a very large time and money investment to get a good sample.

Unfortunately, our sample is a “convenience sample”. Our team discussed what it would take to do a “simple random sample” of french fries from these restaurants, and it just didn’t seem feasible from a cost or time perspective. We spent around $15 on fries, and it took us around 4 hours to measure and gather our data. Getting a good “simple random sample” would easily require 10 times the money and time. This revealed to us that getting a good sample of data is difficult.

Fries were collected during the last week of March 2022. A researcher would place the fry on a scale and read the weight visible on the scale. The scale is an Ozeri ZK14-S Pronto digital kitchen and food scale. The scale is accurate from 0 to 5100 grams. The scale has a precision to 1 gram (0.04 oz). A second researcher would input the data into a .csv file. Fry On Scale

The researcher will then take the fry and measure it’s length. The measurement device is a stainless steel millimeter/inch ruler that is 6 inches long. If the fry is curved the researcher would extend the fry until straight. The researcher would then measure the center of the fry by the height and width and state the two numbers. As before, a second researcher would input those values into the .csv file. A single fry was longer than the measuring tape. This specific fry was measured to the entire length then shifted to measure the remaining length. Each fry was placed directly on the measuring ruler then visually measured.

Fry Measured By Length

The weight and cost of each large fry can be seen below:

Measuring each fry from the four companies provided data from over 300 fries with over 1200 data points. Weights were collected in ounces, the ounces were converted to grams due to the scale’s accuracy. While weight and dimension are continuous variables, we obtained discrete data due to limitations in our measurement instruments. While measuring, the scale would occasionally oscillate between two weight values; for example, 1 or 2 ounces. Because the accuracy of the scale was low, the weight data has discrete qualities.

Evaluating the data will consist of visualizing each company’s measured large fry population values to find possible trends. Then we will get statistical data to evaluate what the average fry is for each company. This includes measured data like weight and calculated values like density and volume. Assuming the data that we collected is somewhat normally distributed, we will use a t-test with a 95% confidence interval to compare the restaurant’s fries.

Data Analysis

In data analysis we will provide averages, volume, dimensions, weight accuracy and mass calculations.

Average Fry Statistics

We composed the following two tables. The first one shows the overall statistics of the large fry order. These are not great reference points because we only obtained one large from each company. However, we can get some of the picture from the first table. The second table is more interesting because it shows the average fry from each company and will be the basis of most of our analysis.

The Average Fry Dimensions
Company Grams Length Height Width Density
McDonalds 1.831579 67.41053 5.031579 4.905263 0.0010798
Wendy’s 1.784946 62.88172 5.870968 7.247312 0.0006287
Burger King 3.854167 81.95833 7.562500 7.437500 0.0008136
Carl’s Jr. 1.670732 65.37805 6.097561 6.085366 0.0007162
Large Fries: Fry Count, Cost, Price Per Gram, and Price per Fry
Company FryCount CostPerFry CostPerGram
McDonalds 95 0.0387368 0.0198919
Wendy’s 93 0.0336559 0.0173889
Burger King 48 0.0739583 0.0195055
Carl’s Jr. 82 0.0392683 0.0213245

These values are the average measured results, as well as a calculation for density. However, there is a flaw from the way we collected the data. We measured width and height interchangeably since the base of each fry is approximately a square. Because of this, all restaurants have similar width and height averages except Wendy’s. Wendy’s has about a millimeter and a half of difference between the height and the width of the fry. If we were to repeat this study, we would make height the larger dimension to avoid this issue again of a non-square fry.

Looking at the statistics above shows that all of the fries are fairly similar except Burger King. Burger King has fries over two times the weight, over 10 mm longer, and thicker than other restaurants. However, they are less dense than McDonalds. Wendys appears to have the least dense fries, with Carls Jr. coming in third. Wendy’s fries are just over half as dense as McDonalds.

Nevertheless, the value we care most about is density. Density should not be affected by the width and height components, because they are both treated as equals. We believe that density is better because it balances the size and weight of each fry. It allows us to look at a comparison of the fries that are long and skinny as equally as the fries that are thick and short. To get a good picture of density, we will first evaluate volume, then mass.

See below for the average dimensions of fries between the companies.

Average Fry Dimensions (millimeters)

Volume

We wanted to graph each of the measured results as well as volume. We were curious if the individual measurements would give us insight along with the combined volume. We Graphed the length, width, and height, then multiplied them to get the volume. We graphed them all with similar code to what follows:

ggplot(fries) +
  geom_density(aes(x=Length, fill=Business), alpha=0.5) +
  labs(
    title="Length of Fries",
    x="Length (mm)"
  ) +
  theme_gray()

Immediately, when looking at these four graphs, you can see how accurate McDonalds slices their fries. Both the height and the width of nearly every fry is 5mm. McDonalds definitely has the most consistency when it comes to the way the cut their fries. Looking at all four graphs and the statistics from earlier, it is clear that Burger King has a different fry then the other brands. Burger king has longer and thicker fries then the other companies.

Weight and Accuracy

As a sanity check, we measured the weight of all the fries individually as well as the fries as a whole. The following table shows the comparison:

Combined Weight vs. Individual Weights Summed
Location Wendy’s Burger King McDonalds Carl’s Jr
Combined Weight 180 182 185 151
Individual Sums 166 185 174 137

The combined weight of the collective fries was different than the weight of all fries combined. Combining all values results in a standard deviation of 10.5 grams among all the fries. This indicates a standard deviation, or error of 0.0330189 grams per fry. While we believe the singular measured weight of all of the fries to be the most accurate, our low sample size of “fry orders” prevents us from calculating a per-fry value. The error is fairly large because of the inaccuracy of our scale in measuring low-weight values. For the remainder of the data collected we will analyze the data assuming no weight measurement error.

We graphed the weight in a similar format as above: 

## 
##  Welch Two Sample t-test
## 
## data:  justbk$Grams and justmcd$Grams
## t = 7.2624, df = 57.33, p-value = 1.128e-09
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.464967 2.580208
## sample estimates:
## mean of x mean of y 
##  3.854167  1.831579

This picture is roughly the same. Burger King has a very normal distribution with heavier, but fewer fries. McDonalds seems to have more fries of a higher weight than Wendy’s or Carls Jr. However, these three seem to have very similar weights. Looking at density will hopefully negate the gap in approach between Burger King and the other three brands.

Density

## 
##  Welch Two Sample t-test
## 
## data:  justbk$Density and justmcd$Density
## t = -5.0423, df = 115.46, p-value = 1.724e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.0003708133 -0.0001616500
## sample estimates:
##   mean of x   mean of y 
## 0.000813567 0.001079799

We have finally arrived to density. This graph is different from all the others because it puts mass in relation volume. Looking at the above graph shows that McDonalds has a denser fry on average. Burger king has the most consistent density in fry at second place. Wendy’s also has a fairly consistent fry. Carl’s Jr. has less consistency, but typically the same average density as the other fries.

Performing a one-way analysis of means, we check to see if we have 95% confidence that the grams between the fries is normally distributed between the fries.

## 
##  One-way analysis of means
## 
## data:  Grams and Business
## F = 48.092, num df = 3, denom df = 314, p-value < 2.2e-16

As p-value is well below 0.05 we reject the hypothesis that the grams are similar. This is interpreted to mean that grams vary between businesses.

Another question using a one-way analysis of means is the density. Do the densities appear to be from a similar population?

## 
##  One-way analysis of means
## 
## data:  Density and Business
## F = 36.788, num df = 3, denom df = 314, p-value < 2.2e-16

Note that he F value is 36. This means that the variance between businesses is less for density than mass. The p-value is once again far below 0.05. This is a very interesting result, as it seems to indicate that the restaurants use different kinds of potatoes with different densities. We expected that the average density between the restaurants would be very similar, since all fries are made with potatoes.

Study Limitations

As previously discussed, multiple limitations exist in this study. Limitations and recommendations for future studies are provided below.

Conclusions

Multiple fries were compared among Burger King, McDonald’s, Wendy’s and Carl’s Jr. Below are distinguishing properties between the businesses.

After performing a test of variance it was determined that the businesses have less variance in density than mass. We surmise that the density, though different, is more similar because fries are using potatoes. The interesting thing to note is that three businesses are similar in density and McDonalds has a more dense fry. While this is conjecture, it could be a different potato or process that would distinguish McDonalds from the other companies.